Abstract [en]

We consider the nonlinear Schrodinger equation on the half-line with a given Dirichlet (Neumann) boundary datum which for large t tends to the periodic function g(0)(b)(t) (g(1)(b)(t)). Assuming that the unknown Neumann (Dirichlet) boundary value tends for large t to a periodic function g(1)(b)(t) (g(0)(b)(t)), we derive an easily verifiable condition that the functions g(1)(b)(t) and g(0)(b)(t) must satisfy. Furthermore, we propose two different methods, one based on the formulation of a Riemann-Hilbert problem and the other based on a perturbative approach, for constructing g(1)(b)(t) (g(0)(b)(t)) in terms of g(0)(b)(t) (g(1)(b)(t)).